A thin, flat circular loudspeaker diaphragm of radius has surface density , where is…

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Calculus of change and accumulation · Calculus of change and accumulation

Mathematical Methods for Physics, Ch Multiple integrals and change of variables

Problem

A thin, flat circular loudspeaker diaphragm of radius R=0.50 mR = 0.50\,\mathrm{m} has surface density σ(r)=σ0(1−rR)\sigma(r) = \sigma_0\left(1 - \dfrac{r}{R}\right), where rr is the distance from the centre and σ0=3.0 kg m−2\sigma_0 = 3.0\,\mathrm{kg\,m^{-2}} is the density at the centre. Using plane polar coordinates with the Jacobian ∣J∣=r|J| = r, find the total mass of the diaphragm.

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